The new Nemesia cultivar is a product of a planned breeding program conducted by the inventor, Gabriel Danziger, in Moshav Mishmar Hashiva, Israel. The objective of the breeding program was to produce new varieties of Nemesia for commercial introduction. The seed parent is the unpatented, proprietary seedling variety referred to as Nemesia fruticans ‘NE-Z-21.’ The pollen parent is unknown as the new variety is the result of an open pollination in which the male parent cannot be identified. The new variety was discovered in April 2006 by the inventor in a group of seedlings resulting from that crossing, in a commercial greenhouse in Moshav Mishmar Hashiva, Israel. Asexual reproduction of the new cultivar ‘Dannemes4’ by vegetative cuttings was first performed at a commercial greenhouse in Moshav Mishmar Hashiva, Israel in September 2006. Subsequent propagation has shown that the unique features of this cultivar are stable and reproduced true to type on successive generations.